It must be hardware, suitable for live performance... though reliable hardware interface with the above as a dedicated (or easily accessible) purpose is acceptable. A music keyboard is not necessary though.

My apologies if there is some sort of obvious product which fits this description - as I say this is a big gap in my knowledge.

Can you be more specific? What kind of useful sampling interface can you get for the ipad (or other touch device - doesn't need to be ipad as I don't own one yet) which matches my requirements in the OP?

SAMPLR is the name of a specific iPad/iPhone app that a lot of people like. I don't know if it fits all your requirements.

I'm not up 100% on every hardware sampler, but the Roland V-Synth gets a lot of love for extreme sample mangling. I believe it's very good for extreme time stretching/warping and resampling, not so sure about the other stuff.

Frankly you might have a hard time finding something in hardware that fits all those criteria... hardware samplers got capable enough to do all that stuff right around the time soft samplers came along and got popular for easier workflow, and then added a lot of extreme manipulation as well.

The Big 3 really let software in the door by producing hardware grooveboxes/loopers/samplers that always had at least one missing deal-breaker feature, like lack of velocity-sensitive pads, midi, etc... Their logic and motto, I presume, was and is, "always keep them upgrading." When the price and portability of computers dropped no one needed the hassle.

Part of the reason to leave off features is simply price - you can try to undercut your competitors by skipping one or two features you don't think are as important/popular as the rest. I wonder what the balance is/was between that side and the upgrade strategy you mention.